I would place it early 25th century and make it a show with TNG's idealism and sense of exploration but contrasted against the realpolitik of DS9.
I agree there is the risk of technology getting too magical and too plot breaking, but to be blunt, the implications of their technologies have never stopped the writers before from just doing the story they wanted to do. And there's nothing at all stopping them from throwing out everything Voyager and Enterprise established about the 27th through 31st centuries.
Why not have warp technology advance to the point they can reach other galaxies in say, a few months travel, and send a small fleet of ships alone to explore and engage diplomacy in the Andromeda galaxy. Close enough to get home whenever they want, but not so close to get reinforcements in a dangerous situation.